Problem: $g(n) = -n^{2}$ $f(n) = 5n+g(n)$ $h(n) = n^{2}+2n+3(f(n))$ $ h(f(0)) = {?} $
First, let's solve for the value of the inner function, $f(0)$ . Then we'll know what to plug into the outer function. $f(0) = (5)(0)+g(0)$ To solve for the value of $f$ , we need to solve for the value of $g(0)$ $g(0) = -0^{2}$ $g(0) = 0$ That means $f(0) = (5)(0)$ $f(0) = 0$ Now we know that $f(0) = 0$ . Let's solve for $h(f(0))$ , which is $h(0)$ $h(0) = 0^{2}+(2)(0)+3(f(0))$ To solve for the value of $h$ , we need to solve for the value of $f(0)$ $f(0) = (5)(0)+g(0)$ To solve for the value of $f$ , we need to solve for the value of $g(0)$ $g(0) = -0^{2}$ $g(0) = 0$ That means $f(0) = (5)(0)$ $f(0) = 0$ That means $h(0) = 0^{2}+(2)(0)+(3)(0)$ $h(0) = 0$